The speed of the fast plane is 490 mph while the speed of the slow plane is 400 mph
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the speed of the fast plane and y represent the speed of the slow plane.
Their speeds differ by 90mph, hence:
x - y = 90 (1)
The planes meet after 3 hours, hence:
3x + 3y = 2670 (2)
From both equations:
x = 490, y = 400
The speed of the fast plane is 490 mph while the speed of the slow plane is 400 mph
Find out more on equation at: https://brainly.com/question/13763238
#SPJ1
3(19 + 2) The product of 3 and the first term is ________ .
In the expression 3(19 + 2), the product of 3 and the first term is 57.
What is Multiplication or Product of two terms?Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors. Mathematically, the product of two numbers 'a' and 'b' is -
M = a x b
or
M = a + a + a + a +...... b times
Given is the following expression -
3(19 + 2)
We can solve the given expression using the distributive law of addition which says, for three numbers A, B and C →
A(B + C) = (A x B) + (A x C)
Using the distributive law of addition -
3(19 + 2)
3 x 19 + 3 x 2
57 + 6
In the expression, 19 is the first term, so the product will be 57.
Therefore, in the expression 3(19 + 2), the product of 3 and the first term is 57.
To solve more questions on Simplifying Expressions , visit the link below-
https://brainly.com/question/22501416
#SPJ1
Write the equation of each line in slope-intercept form.
The line parallel to y=-3x + 4 that passes through (9,-6).
O y = 3x + 21
Oy=-3x+4
Oy=-1/3x + 27
Oy=-3x + 21
The fourth option:
y=-3x+21 is correct.
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{-3} x+4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we're really looking for the equation of a line whose slope is -3 and that it passes through (9 , -6)
[tex](\stackrel{x_1}{9}~,~\stackrel{y_1}{-6})\hspace{10em} \stackrel{slope}{m} ~=~ - 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{- 3}(x-\stackrel{x_1}{9}) \implies y +6= -3 (x -9) \\\\\\ y+6=-3x+27\implies {\LARGE \begin{array}{llll} y=-3x+21 \end{array}}[/tex]
Which of the following describes the translation shown? A. T₍₁₁, ₅₎ B. T₍₋₁₁, ₋₅₎ C. T₍₋₁₁, ₅₎ D. T₍₁₁, ₋₅₎
The translation of a point a units right and b units down is given by [tex]T_{(a,-b)}[/tex]
What is a triangle?A triangle is a polygon that has three angles and three sides. The sum of angles in a triangle is 180 degrees. Types of triangles are isosceles, equilateral and scalene
Translation is the movement of a figure either up, right, left or down in the coordinate plane. Translation, reflection and rotation are rigid transformations while dilation is not a rigid transformation.
The translation of a point a units right and b units down is given by [tex]T_{(a,-b)}[/tex]
Find out more on triangle at: https://brainly.com/question/17335144
#SPJ1
The second of two numbers is 5 more than twice the first. Their sum is 80. Find the numbers.
Answer:
The numbers are 25 & 55
Step-by-step explanation:
You can quantify this problem by using x to take the place of the first number. Because x is multiplied by 2 we get 2x, and add 5 since it is 5 more than twice the first. We can add x to 2x+5 which is 3x+5 and set it equal to 80. Then solve for x to get your first number, and subtract 80 from x to get your second number. Your work should look like this.
[tex]x + 2x + 5 = 80\\3x + 5 = 80\\3x = 80-5\\3x = 75\\3x/3 = 75/3\\x = 25\\80 -25 = 55[/tex]
Hope this helps!
For the pair of supply-and-demand equations, where x represents the quantity demanded in units of 1000 and p is the unit price in dollars, find the equilibrium quantity and the equilibrium price. 2x+ 9p−90 = 0 and 3x−11p+ 61 = 0
simplify the following expressions 1.)4m+14n+15m 2.)10s(17s-3) 3.) 5-12(17-6k) 4.)6p-9pq+4+q+2pq 5.) -19c -4c+9+16c 6.)16(-8t+10)+18t
hope this helps
Answer:
1.)19m+14n
2.)170^2-30s
3.)-199+72k
4.)-7pq+6p+q+4
5.)-7c+9
6.)-110t+160
Step-by-step explanation:
1
2
3
Hours (h)
1
The table shows the relationship "Kevin read 35 pages per hour."
23
3
4
4
5
5
Pages (p)
35
70
105
140
175
Answer:
variable h is independent
HELP ME 60 POINTS PLEASE HELP ME!!!! Tell me what you know about slope. be as detailed as possible and write in complete sentences in paragraph form. Some examples you can expand on would be slope of parallel and perpendicular lines, finding slope on a graph, using slope formula, etc.
Answer:
The slope is defined as the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run. the form of a rise and run looks like a fraction. The slopes of perpendicular lines are negative reciprocals of one another. For example, a line with a slope of 23 will be perpendicular to a line with a slope of −32 . A line with a slope of -5 will be perpendicular to a line with a slope of 15 .
I hope I helped with your essay <3
Answer:
The slope is finding the rate of increase or decrease in a line. The slope of a line can be helpful in multitudes of problems. One example is the fact that if you multiply the slope of two lines that are perpendicular to each other, you get -1. This way, you can find the slope of a perpendicular line without actually having to calculate it. Another way to use slope is with parallel lines. Parallel lines have the same slope and you can find the equation of another parallel lines just by knowing its slope and one point on that line.
The 12 students in the Environmental Club represent 25% of the students in the seventh grade. How many students are in the seventh grade?
Answer:
Step-by-step explanation:
your answer is going to look like this 12 students represents..............20%5*12=60 represent ......................100%
Answer: 60
Step-by-step explanation:12=25% 24=50% 48=75% 60=100%
find the number of rectangles and squares an 8 by 8 chess board respectively.
Answer:
1296
Step-by-step explanation:
number of horizontal lines in chess board is = 9
number of vertical lines in chess board is = 9
36 x 36 = 1296
The length of a rectangle is three times its width. If the perimeter is 132 inches, what is the length of the rectangle?
1. 48 inches
2. 16.5 inches
3. 49.5 inches
4. 18 inches
Please give an explanation (Do not just give an answer and take points or you will get reported)
Thank you :D
Answer:
Let 2w = the length
P = 2l + 2w
132 = 2(2w) + 2w
132 = 4w + 2w
132 = 6w
22 feet = w
2w = 2(22) = 48 inches
A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all four vertices are equal to 90 degrees.
The length of the rectangle is 49.5 inches.
What is a rectangle?A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all four vertices are equal to 90 degrees.
We have,
Length of a rectangle = L
Width of the rectangle = W
L = 3W _____(1)
The perimeter of the rectangle:
P = 2 ( L + W )
132 = 2 ( L + W )
132 / 2 = L + W
66 = L + W
From (1),
66 = 3W + W
66 = 4W
66/4 = W
W = 16.5 inches.
From (1),
L = 3 x 16.5
L = 49.5 inches
Thus the length of the rectangle is 49.5 inches.
Learn more about rectangles here:
https://brainly.com/question/9387981
#SPJ2
Josiah says to Mia, If you give me $8.50, we will have an equal amount of money." Mia responds, "That may be true, but if you give me $8.50
instead, I will have twice as much money as you." How much money did Josiah and Mia each have in the beginning?
Josiah and Mia have $42.5 and $59.5 in the beginning respectively.
How to find the how much money did Josiah and Mia each have in the beginning?Let us assume x is the amount that Josiah have in the beginning.
y is the amount that Mia have in the beginning.
from the question
if Mia gives $8.50 to the Josiah then both have equal amount which means
y - 8.50 = x + 8.50 ........................(1)
now Mia has double If Josiah gives Mia $8.50 which means
y + 8.50 = 2(x - 8.50)
y + 8.50 = 2x - 17 ..........................(2)
now subtract equation (1) from equation (2)
(y - 8.50) - (y + 8.50) = (x + 8.50) - (2x - 17)
y - 8.50 - y - 8.50 = x + 8.50 - 2x + 17
-17 = -x + 25.5
-x = -25.5-17
x = 42.5
now put x value into equation (1) to obtain y value
y - 8.50 = x + 8.50
y - 8.50 = 42.5 + 8.50
y = 51 + 8.50
y = 59.50
Hence, the Josiah and Mia have $42.5 and $59.5 in the beginning respectively.
Learn more about algebraic equations from here:
https://brainly.com/question/4541471
#SPJ9
helpppppppppppppppppppp
Answer:
other answer is right
Step-by-step explanation:
a number has 8 in the tens place, 5 in the thousands place,2 in the ones place, and 3 in the hundreds place. what number am I?
According to the given information, the number is 5382.
What are numbers?An arithmetic value used to represent quantity is called a number. A number is a mathematical concept that is used for counting, measuring, and labeling. Thus, mathematics is built on numbers. For instance, this is a single butterfly, and there are four. A number is a fundamental mathematical unit. For counting, measuring, and comparing quantities, we use numbers. A set of symbols, or numerals, used to represent numbers is known as a number system. The ten symbols known as digits—0, 1, 2, 3, 4, 5, 6, 7, 8, and 9—as well as combinations of these digits make up the most widely used number system.So, the number:
8 in the tens place = xx8x5 in the thousands place = 5x8x2 in the one place = 5x823 in the hundreds place = 5382Therefore, the number is 5382.
Know more about numbers here:
https://brainly.com/question/25734188
#SPJ9
The area of a circle is 2122.64 sq cm. What is the circumference?
*explain in words*
the circumference of circle of area 2122.64 sq. cm. is 163.36 cm.
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
Area of circle is calculated using formula :
A = πr²
It is given that Area of circle is 2122.64 sq cm. then the radius will be :
A = πr²
2122.64 = π(r)²
r = √2122.64 / π
r = 26 cm
Now, calculating the circumference of the circle using formulae :
C = 2πr
C = 2π x 26
C = 163.36 cm
Therefore, the circumference of circle of area 2122.64 sq cm is 163.36 cm.
Read more about area of circle at:
https://brainly.com/question/472270
#SPJ1
What is the Value of X?
Answer:
8.5
Step-by-step explanation:
180 - 102 = 78
78 + 68 + 4x = 180
146 + 4x = 180
4x = 180 - 146
4x = 34
x = 8.5
Find the inverse of g (x)=1/3x-7 and the. Find it’s domain and range
Im unsure, I just took this test :P
You burn 300 Calories will exercising for 40 minutes. What is your average power while exercising, in watts? Select one: A. 523 watts B. 784.5 watts C. 627.6 watts D. 418.4 watts
Based on the number of calories that you burn after exercising for 40 mins, your average power would be A. 523 watts.
What is your average power?A single calorie is 4.184 Joules
This means that 300 calories will be:
= 300 x 4.184
= 1,255.20 Joules
The power is therefore:
= 1,255.20 / (40min x 60 secs)
= 0.523
= 523 watts
Find out more on average power at https://brainly.com/question/13976868
#SPJ1
David's monthly bank statement showed the following deposits and withdrawals:
$77.25,-$50.11, -$25.45, $79.83, $29.47
If David's balance in the account was $34.35 at the
beginning of the month, what was the account balance at the
end of the month?
Answer:
Step-by-step explanation:
Take the sum of all the components and you will get the account balance
+$77.25
-$50.11
-$25.45
+$79.83
+$29.47
+$34.35 (also add the starting balance
= $145.34
can you combine like terms if there is no exponent, example: 0.65 + 0.35 + 0.40. could you combine the 0.65 and the 0.35.
yes you can do that i looked it up
(3x + 5)° (10x - 7)° R
M QRT =
Using supplementary angles, it is found that the measure of angle QRT is of 47º.
What is the missing information?For this problem, we have a straight line segment QS divided by an inclined segment RT. The measures of the angles are given as follows:
m<QRT = 3x + 5.m<TSR = 10x - 7.What are supplementary angles?When two angles have measures adding to 180º, they are called supplementary.
In this problem, due to the inclined segment, angles QRT and TSR are supplementary, and we can solve for x as follows:
3x + 5 + 10x - 7 = 180
13x = 182
x = 182/13
x = 14.
Hence the measure of angle QRT is found as follows:
m<QRT = 3(14) + 5 = 47º.
More can be learned about supplementary angles at https://brainly.com/question/12919120
#SPJ1
Maria practiced the piano for 2 1/2 hours last week and 1 3/4 hours this week.Use the bar diagram sections to construct a bar diagram that represents how many hours Maria practiced in the past 2 weeks.
How many hours did Maria practice the piano in the past 2 weeks?
The number of hours that Maria practiced in the past 2 weeks will be 4 1/4 hours.
How to illustrate the fraction?From the information, Maria practiced the piano for 2 1/2 hours last week and 1 3/4 hours this week.
Therefore, the number of hours that Maria practiced in the past 2 weeks will be:
= 2 1/2 + 1 3/4
= 2 2/4 + 1 3/4
= 4 1/4 hours
The number of hours that Maria practiced in the past 2 weeks will be 4 1/4 hours.
Learn more about fractions on:
brainly.com/question/17220365
#SPJ1
can someone help me the problems are in the photo there is only 2
Answer:
7.) 135%, 13.5, 8⅗
135% = 135/100 = 1.3513.5 = 13.58⅗= 43/5 = 8.6from least to greatest= 1.35, 8.6, 13.5.
= 135%, 8⅗, 13.5.
8.) ⅙, 16.7%, 0.16
1/6 = 0.166 ≈ 0.17.16.7% = 16.7/100 = 0.167 ≈ 0.170.16 = 0.16from least to greatest= 0.16, 0.17, 0.17
= 0.16, 1/6, 16.7%
**sorry if it's late ...
you could also check it too
Which one of the following radicals cannot be simplified?
√27
√24
√26
√25
Answer:
B and C
Step-by-step explanation:
In terms of square root b and c cannot be simplified to get a whole number answer.
Demonstration:
√24
The answer would be about 4.898
√26
The answer would be about 5.099
Both of these cannot be multiplied by any number to get 26 or 24.
Hence, the answer would be B and C.
what is the reciprocal of 4/8
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{4}{8}}\\\\\mathsf{= \dfrac{8}{4}}\\\\\mathsf{= \dfrac{8\div4}{4\div4}}\\\\\mathsf{= \dfrac{2}{1}}\\\\\mathsf{= 2\div1}\\\\\mathsf{= 2}\\\\\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{2\ or\ \dfrac{8}{4}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Answer:
Reciprocal of 4/8 = 8/4
Step-by-step explanation:
To get the reciprocal of 4/8 based on that definition, we can make the following equation where "R" is the reciprocal of 4/8.
(4/8) × R = 1
When we solve for R, we get the answer to the reciprocal of 4/8 as a fraction as follows:
(4/8) × R = 1
R = 8/4
Reciprocal of 4/8 = 8/4
−4(x−3)−1=4−7(x−5) solve for x
Answer:
9.33
Step-by-step explanation:
[tex]-4(x-3)-1 = 4-7(x-5)\\-4x+12-1 = 4-7x+35\\-4x+7x = -12+1+4+35\\ 3x = 28\\x = 28/3\\x = 9.33[/tex]
the line on a graph passes through the points (1,3) and (7,1)
The midpoint of the points (1,3) and (7,1)
M=(2,4)
This is further explained below.
What is the midpoint of points (1,3) and (7,1)?Generally, the equation for is midpoint mathematically given as
[tex]M=\frac{x1-x2}{2}, \frac{y1-y2}{2}[/tex]
Therefore
[tex]M=\frac{1+3}{2}, \frac{7+1}{2}[/tex]
M=(2,4)
In conclusion,the midpoint of points (1,3) and (7,1)
M=(2,4)
Read more about midpoint
https://brainly.com/question/28224145
#SPJ1
CQ
The line on a graph passes through the points (1,3) and (7,1)
What is the midpoint of the points
Below is the graph h(x)h(x)h, left parenthesis, x, right parenthesis. The function intersects its midline at (0.5,-3)(0.5,−3)left parenthesis, 0, point, 5, comma, minus, 3, right parenthesis and has a minimum point at (-1.5,-8)(−1.5,−8)left parenthesis, minus, 1, point, 5, comma, minus, 8, right parenthesis. Find a formula for h(x)h(x)h, left parenthesis, x, right parenthesis. Give an exact expression
The sine function h(x) is given by:
h(x) = 5sin(π/4(x - 0.5)) - 3.
What is the sine function?The cosine function is defined as follows:
g(x) = asin(bx+c)+d.
The coefficients have these following roles:
a: amplitude.b: The period is of 2π/B.c: phase shift.d: vertical shift.For this function, we have that:
The midline is of -3.The minimum value is of -8.Hence the coefficient a is of 5, as:
a = -3 - (-8) = -3 + 8 = 5.
A standard cosine function with amplitude 5 would vary between -5 and 5, with midline at 0, hence the coefficient d is of d = -3.
The minimum value and midline form one-fourth the period, hence, since the period is of 4 x (0.5 - (-1.5)) = 8, we have that:
2π/B = 8
B = π/4
The standard midline is at x = 0, but for this function function it is at x = 0.5, meaning that the function was shifted 0.5 units right, hence c = -0.5.
Thus the function is given by:
h(x) = 5sin(π/4(x - 0.5)) - 3.
The graph at the end of the answer shows that the function has the desired features.
More can be learned about trigonometric functions at brainly.com/question/21558626
#SPJ1
Find the equation of a line that contains the points (−6,8) and (4,−1). Write the equation in slope-intercept form, using fractions when required.
The slope-intercept form of the equation of the line described is y = -10/9x + 4/3.
Given the following data:
Points on x-axis = (-6, 4).
Points on y-axis = (8, -1).
What is a slope?A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.
How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Substituting the given points into the formula, we have;
Slope = (4 + 6)/-1 - 8)
Slope = -10/9
Mathematically, the standard form of the equation of a straight line is given by;
y = mx + c
Where:
x and y are the points.m is the slope.c is the intercept.At point (-6, 8), we have:
8 = -10/9(-6) + c
8 = 60/9 + c
72 = 60 + 9c
9c = 72 - 60
c = 12/9
c = 4/3
Therefore, the slope-intercept form of the equation of the line described is y = -10/9x + 4/3.
Read more on slope-intercept form here: brainly.com/question/1884491
#SPJ1
A machine at a bakery is pouring out flour. The graph shows the amount of flour (in grams) in the machine versus time (in minutes).
(a) What is the amount of flour in the machine at minutes?
(b) Choose the statement that best describes how the time and amount of flour are related. Then fill in the blank.
As time increases, the amount of flour in the machine decreases.
At what rate is the amount of flour decreasing?
As time increases, the amount of flour in the machine increases.
At what rate is the amount of flour increasing?
What is the scatterplot?
We can see that that the data is plotted on a scatterplot. The scatter plot has a vertical and a horizontal axis. It is evident that the horizontal axis plots the time while what is plotted on the vertical axis is the amount of flour.
As we can see, the relationship between the time and the amount of flour is negative. This can be seen from the shape of the plot as it is displayed in the image attached.
Looking at the shape of the graph, we can see that; The amount of flour when the time is zero seconds is 630 grams. As time increases, the amount of flour in the machine decreases. This corresponds to a negative relationship between the two variables.
The negative relationship also implies that we have to expect to have a negative slope. The rate at which the amount of flour increasing is; 210 – 630/3 – 0 = -140 grams/minute
Learn more about scatter plot:https://brainly.com/question/13984412
#SPJ1